Marinate the quail in olive oil, thyme, and sage for at least 2 hours, up to overnight, in the refrigerator.
Preheat a grill. Preheat the oven to 400 degrees F.
Remove the quail from the marinade and season with salt and pepper. Place the quail, breast-side-up, on a medium hot grill. Cook for 3 minutes, then turn over so the breast-side is down, and cook for 2 minutes. Then lift and adjust position on the grill to create an "x" mark on the breast. Finish cooking for about 4 minutes, about 8 to 9 minutes total cooking time.
While the quail are cooking, sear the foie gras in a dry, medium-hot pan. Place in the oven for 4 minutes. Remove from the oven, place the foie gras on a cutting board and slice into 8 pieces. Lightly toast the brioche, place a piece of foie gras on each half and a quail on top. Spoon the sauce over the quail and garnish with Sweet Potato Shoestrings.
Place the shallots, wine, and vinegar in a small pot. Bring to a boil, the reduce the heat and simmer until reduced by half. Add the stock and continue to reduce until you have about 1/2 cup of liquid left. Whisk in the jelly, then add the butter and season, to taste. The sauce should be glossy and syrupy, but not too sweet. Add a drop of vinegar, to balance, if necessary. Set aside and keep warm.
Bake the sweet potatoes until very soft. Let cool. Peel and weigh out 12 ounces. Put the sweet potatoes in the bowl of an electric mixer. Using a paddle, mix for 2 minutes on medium speed or until mashed. Then add egg, milk, and yeast and mix for 1 minute. Add the rest of the dry ingredients and mix for 6 minutes on medium speed. Let rest for 15 minutes.
Preheat the oven to 325 degrees F. Add the cold butter in stages on speed 2. Mix for 6 to 8 minutes to smooth out the brioche, until it does not stick to the sides of the bowl. Divide into 2-ounce balls and place in muffin tins or brioche molds. Let rest in a warm place for 1 1/2 hours. Brush with egg wash and bake until golden brown, about 10 minutes.
Preheat a fryer to 325 degrees F. Add the potatoes and fry until crispy. Drain on paper towels and season with salt.